[Paper Review] Scalar decay into pions via Higgs portal

Dmitry Gorbunov, Ekaterina Kriukova+1 more|arXiv (Cornell University)|Mar 22, 2023

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper resolves a long-standing uncertainty in scalar decay rates into pions in Higgs portal models by using gravitational form factors from $ar{ u} u$-mediated $ar{ u} u$ processes, reducing the theoretical uncertainty from a factor of 100 to about a factor of 2. The result shows a smooth transition between pion and gluon decay modes around 1.5–2 GeV, enabling more accurate predictions for future experimental sensitivities.

ABSTRACT

In extensions of the Standard Model (SM) of particle physics a light scalar from a hidden sector can interact with known particles via mixing with the SM Higgs boson. If the scalar mass is of GeV scale, this coupling induces the scalar decay into light hadrons, that saturates the scalar width. Searches for the light scalars are performed in many ongoing experiments and planned for the next generation projects. Applying dispersion relations changes the leading order estimate of the scalar decay rate into pions by a factor of about a hundred indicating the strong final state interaction. This subtlety for about thirty years prevented any reliable inference of the model parameters from experimental data. In this Letter we use the gravitational form factor for neutral pion extracted from analysis of $γ^*γ oπ^0π^0$ processes to estimate the quark contribution to scalar decay into two pions. We find a factor of two uncertainty in this estimate and argue that the possible gluon contribution is of the same order. The decay rate to pions smoothly matches that to gluons dominating for heavier scalars. With this finding we refine sensitivities of future projects to the scalar-Higgs mixing. The accuracy in the calculations can be further improved by performing similar analysis of $γ^*γ o K K$ and $γ^*γ oηη$ processes and possibly decays like $J/ψ oγ+ππ$.

Motivation & Objective

• To resolve the long-standing factor-of-100 theoretical uncertainty in scalar decay rates into pions in Higgs portal models.
• To improve the reliability of experimental constraints on scalar-Higgs mixing by accurately estimating the decay width into pions.
• To establish a duality between pion and gluon decay modes in the GeV mass range, where both contribute significantly.
• To provide a robust framework for updating sensitivities of future experiments to light scalar particles.
• To identify key hadronic processes—such as $ar{ u} u$-mediated $ar{ u} u$ scattering and $J/\psi \to \gamma + \pi\pi$—for further improving decay rate calculations.

Proposed method

• The authors use the gravitational form factor for the neutral pion extracted from analysis of $\gamma^*\gamma \to \pi^0\pi^0$ processes to estimate the quark contribution to scalar decay into two pions.
• They apply dispersion relations to account for final-state interactions, correcting leading-order estimates by a factor of ~100, which had previously hindered reliable parameter inference.
• The method incorporates next-to-leading-order (NLO) QCD corrections and Chiral Perturbation Theory (ChPT) for consistency checks, particularly in the low-mass regime.
• The analysis includes a comparison with existing results from Donoghue et al. (1990) and Bezrukov & Gorbunov (2010), showing no peak-like structures due to light scalar resonances.
• The authors estimate the gluonic contribution to be of the same order as the quark contribution, justifying a combined treatment.
• They validate the result by showing that the pion decay width smoothly matches the gluon decay width around $M_S \sim 1.5-2$ GeV, indicating a quark-gluon duality in hadronic decays.

Experimental results

Research questions

• RQ1 What is the correct decay rate of a light scalar into two pions in Higgs portal models, given the long-standing uncertainty of ~100× in previous estimates?
• RQ2 How do final-state interactions and non-perturbative QCD effects influence the scalar decay width into pions?
• RQ3 To what extent do the quark and gluonic contributions to scalar decay into pions balance each other in the GeV mass range?
• RQ4 Can the gravitational form factor from $\gamma^*\gamma \to \pi^0\pi^0$ be reliably used to estimate the scalar decay amplitude into pions?
• RQ5 How do the updated decay rates affect the projected sensitivity of future experiments to the scalar-Higgs mixing parameter $\xi$?

Key findings

• The theoretical uncertainty in the scalar decay rate into pions is reduced from a factor of ~100 to a factor of ~2 by using gravitational form factors from $\gamma^*\gamma \to \pi^0\pi^0$ processes.
• The decay width into pions smoothly matches the width into gluons for scalar masses around 1.5–2 GeV, indicating a duality between quark and gluonic contributions.
• The quark contribution to the scalar decay into pions is estimated with a factor-of-two uncertainty, and the gluonic contribution is found to be of the same order of magnitude.
• The model does not exhibit peak-like structures in the decay rate due to light scalar resonances such as $f_0(500)$ or $f_0(980)$, which are either broad or not dynamically significant in this context.
• The inclusion of the corrected pion decay width significantly improves the accuracy of branching ratio predictions and updates the expected reach of future experiments in the scalar-Higgs mixing parameter space.
• Further improvements in accuracy are expected by analyzing additional processes such as $\gamma^*\gamma \to KK$, $\gamma^*\gamma \to \eta\eta$, and $J/\psi \to \gamma + \pi\pi$.